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Signal detection theory or Detection theory, is a means to quantify the ability to discern between signal and noise. According to the theory, there are a number of psychological determiners of how we will detect a signal, and where our threshold levels will be. Experience, expectations, physiological state (e.g. fatigue) and other factors affect thresholds. For instance, a sentry in wartime will likely detect fainter stimuli than the same sentry in peacetime.
Much of the early work in detection theory was done by radar researchers. Detection theory was used in 1966 by John A. Swets and David M. Green for psychophysics. Green and Swets criticized the traditional methods of psychophysics for their inability to discriminate between the real sensitivity of subjects and their (potential) response biases.
Detection theory has applications in many fields such as diagnostics of any kind, quality control, telecommunications, and psychology. The concept is similar to the signal to noise ratio used in the sciences, and it is also usable in alarm management, where it is important to separate important events from background noise.
Signal detection theory (SDT) is used when psychologists want to measure the way we make decisions under conditions of uncertainty, such as how we would perceive distances in foggy conditions. SDT assumes that the decision maker is not a passive receiver of information, but an active decision-maker who makes difficult perceptual judgements under conditions of uncertainty. In foggy circumstances, we are forced to decide how far away from us an object is based solely upon visual stimulus which is impaired by the fog. Since the brightness of the object, such as a traffic light, is used by the brain to discriminate the distance of an object, and the fog reduces the brightness of objects, we perceive the object to be much further away than it actually is (see also Decision theory).
To apply signal detection theory to a data set where stimuli were either present or absent, and the observer categorized each trial as having the stimulus present or absent, the trials are sorted into one of four categories:
Respond "Absent" Respond "Present" Stimulus Present Miss Hit Stimulus Absent Correct Rejection False Alarm
Based on the proportions of these types of trials, numerical estimates of sensitivity can be obtained with statistics like the sensitivity index d' and A', and response bias can be estimated with statistics like β.
Sensitivity or discriminability
Conceptually, sensitivity refers to how hard or easy it is to detect that a target stimulus is present from background events. For example, in a recognition memory paradigm, having longer to study to-be-remembered words makes it easier to recognize previously seen or heard words. In contrast, having to remember 30 words rather than 5 makes the discrimination harder. One of the most commonly used statistics for computing sensitivity is d'. There are also non-parametric measures.
Bias is the extent to which one response is more probable than another. That is, a receiver may be more likely to respond that a stimulus is present or more likely to respond that a stimulus is not present. Bias is independent of sensitivity. For example, if there is a penalty for either false alarms or misses, this may influence bias. If the stimulus is a bomber, then a miss (failing to detect the plane) may increase deaths, so a liberal bias is likely. In contrast, crying wolf (a false alarm) too often may make people less likely to respond, grounds for a conservative bias.
- Constant false alarm rate
- Estimation theory
- Just noticeable difference
- Likelihood-ratio test
- Neyman-Pearson lemma
- Psychometric function
- Psychophysical measurement
- Receiver operating characteristic
- Statistical signal processing
- Threshold determination
- Visual search
- ↑ Marcum, J. “A statistical theory of target detection by pulsed radar”, IEEE Trans. Info. Thry., Apr. 1960.
- ↑ Swets, J.A. (ed.) (1964) Signal detection and recognition by human observers. New York: Wiley
- ↑ Green, D.M., Swets J.A. (1966) Signal Detection Theory and Psychophysics. New York: Wiley. (ISBN 0-471-32420-5)
- Coren, S., Ward, L.M., Enns, J. T. (1994) Sensation and Perception. (4th Ed.) Toronto: Harcourt Brace.
- Kay, SM. Fundamentals of Statistical Signal Processing: Detection Theory (ISBN 0-13-504135-X)
- McNichol, D. (1972) A Primer of Signal Detection Theory. London: George Allen & Unwin.
- Van Trees HL. Detection, Estimation, and Modulation Theory, Part 1 (ISBN 0-471-09517-6; website)
- Wickens, Thomas D., (2002) Elementary Signal Detection Theory. New York: Oxford University Press. (ISBN 0-19-509250-3)
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